Determination of RPM from vibration spectral plots

ABSTRACT

A vibration analyzer for use in determining a rotational speed. The vibration analyzer includes: a) an input for sensing vibration data, b) a memory for storing the vibrational data, and c) a processor. The processor 1) produces a spectral plot of the vibrational data, 2) locates peaks in the spectral plot, 3) inputs a rotational speed, and 4) scans the spectral plot in predetermined rotational speed increments to provide a candidate rotational speeds. For each candidate rotational speed i) a number of associated harmonics is identified, ii) closest peaks in the spectral plot to the candidate rotational speed and its harmonics are located, iii) gaps between the closest peaks and the candidate rotational speed and its harmonics are measured, iv) summed, and a sum of the gaps is recorded. In step (5) The candidate rotational speed that is associated with a minimum sum is selected as the nominal rotational speed.

TECHNICAL FIELD

The disclosure relates to the apparatus for the determination ofrotational speed for a machine, and more particularly to analyticalinstruments for determining rotational speed using vibration analysis inthe absence of actual rotational speed measurements.

BACKGROUND OF THE INVENTION

Rotating equipment, such as fans, motors, turbines, and the like, tendto lose their balance or alignment with time due to conditions such aswear, varying load, damage, misuse, and foreign matter accumulation. Asbalance and alignment are lost, the equipment produces excessivevibration, which if left uncorrected, causes accelerated wear and otherdamage to the equipment.

Vibration analyzers detect the vibration emitted from rotatingequipment. Such analyzers determine the source of the vibration, whetherit be imbalance, misalignment, worn bearings, missing or broken parts,or some other problem. To make a proper diagnosis of the vibrationproblem, the rotational speed of the shaft must be known. However, therotational speed is not often known at the time of data collection.Therefore, the rotational speed must be calculated from the vibrationspectrum.

Correlation of the rotational speed of the shaft in the vibrationspectrum is required for problem diagnosis because there are often manydifferent potential sources of vibration, each of which creates adifferent vibration signature. One of the first determinations to bemade is whether the vibration detected is synchronous or asynchronouswith the rotation of the equipment. If asynchronous, an analysis is madeto determine if the vibration can be correlated in some other way to therotational speed of the equipment. In this manner, specific problems areisolated and corrected.

For example, in a piece of rotary equipment such as a turbine, vibrationthat is synchronous with the first harmonic of the rotation speedindicates rotor imbalance, for which there are well defined methods ofcorrection. Knowing the rotational speed of the turbine allows for aspeedy diagnosis of this problem, and reduces time wasted oninvestigation of unrelated potential vibration sources.

As another example, a defective anti-friction bearing produces vibrationthat has a fixed, but non-integer relationship to the speed of theshaft. Thus the vibration is not a harmonic of the rotational speed ofshaft. However, with a knowledge of the bearing parameters, such as theinner and outer raced fault frequencies, the vibration produced by thedefective bearing is correlated with the speed of the shaft, and theproblem is diagnosed and corrected. Again, without knowledge of thespeed of the shaft, the defective bearing is more difficult to diagnose.

Further, in a piece of rotary equipment such as a gear box, which mayhave several gears of different sizes, a problem such as a cracked toothon one of the gears creates vibration that is synchronous with therotational speed of a shaft. Correlating the speed of rotation, theknown number of teeth on each gear, and the vibration spectrum allowsthe damaged gear to be diagnosed.

In each case, the diagnosis of the source of vibration is made easier ifthe rotational speed of the equipment is known. The actual correlationof the rotational speed to the vibration spectrum, and the analysis ofthe correlated information, is performed either by the technician, orautomatically by the vibration detection instrument, if it has suchcapability.

The problem is that without use of a tachometer to measure therotational speed it is difficult to determine the rotational speedaccurately. In many cases, the rotational speed is either assumed to bethe default assigned when the machine was configured or is manuallyentered when data is collected using a portable analyzer. In suchsituations, the rotational speed is at best an approximation. As theload on the machine varies, the actual rotational speed may also vary.Thus the assumed rotational speed may be completely incorrect due tomanual data entry errors. What is needed, therefore, is an apparatusthat can be used to determine the rotational speed of a machine when atachometer and actual rotational speed data are unavailable.

SUMMARY OF THE INVENTION

In view of the foregoing, a first aspect of the invention is a vibrationanalyzer for use in determining a nominal rotational speed of a rotatingshaft. The vibration analyzer includes: a) an input for sensingvibration signal data at an unknown rotational speed of the shaft, b) amemory for storing the vibrational signal data, and c) a processor. Theprocessor 1) produces a spectral plot of the vibrational data, 2)locates peaks in the spectral plot, 3) inputs a rotational speed, and 4)scans the spectral plot in predetermined rotational speed incrementsbeginning at a first rotational speed and ending at a second rotationalspeed to provide a candidate rotational speed at each increment. Foreach candidate rotational speed i) a predetermined number of associatedharmonics is identified, ii) closest peaks in the spectral plot to thecandidate rotational speed and its associated harmonics are located,iii) gaps between the closest peaks and the candidate rotational speedand its associate harmonics are measured, iv) the gaps in associationwith the candidate rotational speed are summed, and a sum of the gaps isrecorded. In step (5) The candidate rotational speed that is associatedwith a minimum sum in step (iv) is then selected as the nominalrotational speed.

In a second aspect of the invention, there is provided a vibrationanalyzer for use in determining a nominal rotational speed of a rotatingshaft. The vibration analyzer includes: a) an input for sensingvibration signal data at an unknown rotational speed of the shaft, b) amemory for storing the vibrational signal data, and c) a processor. Theprocessor 1) produces a spectral plot of the vibrational data, 2)locates peaks in the spectral plot, and 3) scans the spectral plot inpredetermined rotational speed increments beginning at a firstrotational speed and ending at a second rotational speed to provide acandidate rotational speed at each increment. For each candidaterotational speed: i) a predetermined number of associated harmonics isidentified, ii) closest peaks in the spectral plot to the candidaterotational speed and its associated harmonics are located, iii) gaps aremeasured, and iv) the sum of the gaps is recorded. Next, (4) the sums ofthe gaps that represent local minimum gaps are identified, (5) peak sumsassociated with the local minimum gaps in step (4) are located, and 6)the candidate rotational speed that is associated with the maximum peaksum in step (5) is selected as the nominal rotational speed.

In a third aspect of the invention, there is provided a vibrationanalyzer for use in determining a nominal rotational speed of a rotatingshaft. The vibration analyzer has an input for sensing vibration signaldata at an unknown rotational speed of the shaft, a memory for storingthe vibrational signal data, and a processor. The processor produces aspectral plot of peaks in the vibrational data; receives an estimatedrotational speed; receives an accuracy value; identifies a predeterminednumber (k) of largest peaks in the spectral plot; and records a locatedamplitude and associated frequency for each peak. A set of candidaterotational speeds is created by dividing the located frequencies of eachof the largest peaks by integer values of 1 through N, where N is amaximum number of harmonics evaluated to calculate the rotational speed,to produce divided values for each of the located frequencies. When agiven one of the divided values is within the accuracy value of theestimated rotational speed, the given divided value is designated as acandidate rotational speed, where each candidate frequency represents aharmonic family. A score is provided for each candidate rotational speedbased on a proximity of the candidate rotational speed and harmonicmultiples of the candidate rotational speed to each of the largestpeaks. The candidate rotational speed with the highest score is selectedas the nominal rotational speed.

In some aspects, the input rotational speed or estimated rotationalspeed is a nameplate rotational speed of the machine.

In other aspects, the first rotational speed is about 50 percent of theinput rotational speed and the second rotational speed is about 150percent of the input rotational speed. In some aspects the firstrotational speed is a rotational speed adjacent a beginning of thespectral plot and the second rotational speed ranges from about ⅕ toabout 1/10 of a total rotational speed range of the spectral plot.

In some aspects, the input for sensing a vibration signal is a vibrationsensor.

In other aspects, the predetermined rotational speed increments rangefrom about 1/10 to about 1/100 of the input rotational speed. In someaspects, the predetermined rotational speed increments range from about1/10 to about 1/100 of a span of the rotational speeds from the firstrotational speed to the second rotational speed.

In the first aspect, a reasonable starting point for the turning speedis identified in the harmonic spectrum. The starting point can come fromthe customer or the literature. The spectrum is scanned in increments ofabout 1% of the starting point, beginning at about 50% of the startingpoint and ending at about 150% of the starting point. The range andincrement is user-adjustable in some embodiments.

In some aspects, the candidate rotational speed is scored by summing agap between each candidate rotational speed and each of the largestpeaks and between each harmonic multiple of the candidate rotationalspeed and each of the largest peaks.

In other aspects, the accuracy value ranges from about 0.5 percent toabout 2 percent.

In still other aspects, the predetermined number of largest peaks in thespectral plot ranges from 1 to K, wherein K is less than or equal toLOR/4, wherein LOR is lines of resolution of the spectral plot.

In other aspects, N typically ranges from about 6 to about 10. The valueof N can be as large as the number of teeth on a gear of a gearbox. Thevalue of N may be an integer value as large as Fmax/(estimated speed)wherein “Fmax” is a maximum frequency.

Accordingly, by using the apparatus described herein a user may be ableto either improve the accuracy of the assumed rotational speed byscanning across the vibrational spectral peaks or, if this does notreflect a reasonable rotational speed, then to scan across all thespectral peaks to determine the most likely rotational speed.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention may best be understood by reference to a detaileddescription of preferred embodiments when considered in conjunction withthe following drawings, in which:

FIG. 1 is a schematic illustration of a vibration analyzer according toembodiments of the disclosure;

FIG. 2 is a block diagram of steps of collecting and using vibrationaldata using an apparatus according to a first aspect of the invention;

FIG. 3 is a graph of peaks in a spectral plot versus rotational speedfor the apparatus according to the first aspect of the invention;

FIG. 4 is a plot of a sum of gaps between peaks and rotational speedsversus rotational speed showing a nominal rotational speed as a minimumsum according to the first aspect of the invention;

FIG. 5 is a block diagram of steps of collecting and using vibrationaldata using an apparatus according to a second aspect of the invention;

FIG. 6 is a graph of vibrational data using an apparatus according to asecond aspect of the invention to find a nominal rotational speed from asum of minimum gaps between a candidate rotational speed and its closestpeak; and

FIG. 7 is a block diagram of steps of collecting and using vibrationaldata using an apparatus according to the third aspect of the invention.

DETAILED DESCRIPTION OF THE INVENTION

The above and other needs are met by an apparatus for use in determiningthe rotational speed of a machine, such as a shaft of a pump, motor,turbine, compressor, gear box, and the like using vibrational data. Suchapparatus, as described in more detail below, may be used in the absenceof a tachometer or nameplate information about the rotational speed ofthe machine.

Vibration analyzers are useful to sense, analyze, and record vibrationin rotating equipment, which vibration can, if left uncorrected, degradethe efficiency of, or even destroy the rotating equipment. Preferably, aportable or hand-held analyzer is used to collect and analyze vibrationdata, which may also be uploaded and stored in a base computer forfurther analysis. Aspects of the invention are not limited to portableor hand-held vibration analyzers, as continuous or on-line analyzers mayalso be used to collect vibration data as well as vibration analysissoftware programs used in post-acquisition analysis of vibration data.

As shown in FIG. 1, a schematic drawing of a vibration analyzer 100,according to aspects of the invention, includes a processor 110, ananalog to digital converter 112, a memory 114, a display device 116, andan alarm device 118. Vibration data from a machine 120 is detected by avibration sensor 122 for input to the vibration analyzer 100 by means ofan analog to digital converter 112. The vibration data is stored in thememory 114 and spectral plots of the data are generated by the processor110 for use in deriving the rotational speed of the machine 120. Oncethe rotational speed of the machine is determined, the vibration datamay be used to determine the source of the vibration so that thevibration can be corrected before damage occurs.

The first aspect of the invention is illustrated by references to FIGS.2-4. FIG. 2 is a block diagram of a procedure 150 for determiningrotational speed, and FIG. 3 is a spectral plot 200 of vibration datagenerated by the processor 110. With reference to FIG. 2, a vibrationdata analysis system is installed in step 152 on the vibration analyzer100. A vibration data database is stored in the memory 114 of theanalyzer 100 in step 154, and a representation of machine 120 locationsand vibration sensors 122 is created in the analyzer memory 114 in step156. Vibration data for the machine 120 is recorded in the database instep 158 using the sensors 122. Using the recorded data, a spectral plot200 of the data is created in step 160 as shown in FIG. 3. In thespectral plot 200, the y-axis represents an amplitude of peaks in theplot 200 and the x-axis represents a frequency in cycles per second or arotational speed in revolutions per minute. It will be appreciated thata frequency may be converted to revolutions per minute and vice versa.Peaks in the spectral plot 200 are located by any conventional peaklocation method in step 162. For example, peaks may be located byinterpolation, summation, or fitting techniques known to those skilledin the art. Each peak in FIG. 3 has associated with it an amplitude(ie., acceleration, velocity, or displacement), or in other words, theenergy present in the movement of the rotating equipment occurring atthat specific frequency.

According to the first aspect of the invention, a starting rotationalspeed 210 is inputted by a user in step 164. The starting rotationalspeed 210 may be selected based on a published rotational speed for themachine 120 or an assumed rotational speed based on comparable machines120. Next, the spectral plot 200 is scanned in step 166 in predeterminedincrements from a point that is slightly less than the startingrotational speed 210 to provide a candidate rotational speed 212. Thecandidate rotational speed 212 is incremented across the spectrum by apredetermined amount to get multiple candidate rotational speeds214-226. For example if a total of 6 to 10 candidate rotational speedsacross the spectrum are selected, the candidate rotational speeds willbe incremented by ⅙ to 1/10 of the total rotational speed span acrossthe spectrum.

Next, peaks 230-244 of the spectrum closest to each of the candidaterotational speeds are identified. The closest peaks may be at rotationalspeeds that are higher or lower than each of the candidate rotationalspeeds. The distances between the peaks and the candidate rotationalspeeds are determined and are defined as gaps 250-264 between the peaks230-244 and the candidate rotation speeds 214-226. Then the harmonics ofthe closest peaks are calculated, and the rotational speed candidates ofthe closest peaks to each of those calculated harmonics of therotational speed candidates are identified in step 172. Once again, thegaps between the rotational speed candidates of the calculated harmonicsand their closest peaks are recorded. In some embodiments, eightcalculated harmonics are used, and in other embodiments the number ofharmonics is user-definable. For each set of candidate rotational speedsand their harmonics, the total of the gaps 250-264 is calculated in step170, stored in the memory 114. The sum of the gaps 250-264 for each setof candidate rotational speeds and their harmonics is plotted versusrotational speed to provide a vee-shaped line having a minimum. FIG. 4illustrates a plot 300 of the sums of the gaps for each increment of thestarting rotational speed. As the candidate rotational speeds increaseas shown by line 310, the sums of the gaps decrease, reach a minimum atpoint 320 and then increase. Point 320 (FIG. 4) is selected as thenominal rotational speed of the machine 120.

In some situations, the input rotational speed may be far removed fromthe actual rotational speed due to, for example input errors. Accordingto the second aspect of the invention, there is no reasonable startingpoint for the turning speed, in which case there is no basis for thestarting and ending points for the scan described in the first aspect ofthe invention. In this aspect of the invention, the scan points startnear zero rotational speed, and extends up to about ⅛th of the totalharmonic spectrum. Turning speed candidates are identified within thisrange as given in the first aspect of the invention, and sums of thegaps for the candidate rotational speeds are calculated.

With reference now to FIGS. 5 and 6, a procedure 400 for determiningrotational speed using the vibration analyzer according to the secondaspect of the invention is illustrated. Steps 402 to 420 are similar tosteps 152 to 170 described above. In step 402, a vibration data analysissystem is installed in the memory 114 of the vibration analyzer 100. Avibration data database is created in the memory 114 to storevibrational data in step 404, and a representation of machine 120locations and vibration sensors 122 is created in the analyzer memory114 in step 406. Vibration data for the machine 120 is recorded in thedatabase in step 408 using the sensors 122. Using the recorded data, aspectral plot 500 of the data is created in step 410 as shown in FIG. 6.In the spectral plot 500, the y-axis represents the value of the sums ofthe gaps determined and the x-axis represents a frequency in cycles persecond or a rotational speed in revolutions per minute. In step 412, thespectral plot 500 is scanned in predetermined rotational speedincrements from a first rotational speed to a second rotational speed toidentify candidate rotational speeds at each increment. Typically fromabout 6 to about 10 rotational increments are used. Next, apredetermined number of harmonics for each candidate rotational speed instep 412 is identified in step 414. In some embodiments, the number ofharmonics ranges from 6 to 10. In other embodiments, the number ofharmonics is defined by the user.

Peaks closest to the candidate rotational speed and its associatedharmonics identified in step 414 are located in step 416 and gapsbetween the peaks and candidate rotational speeds are measured in step418 and summed in step 420. The sums of the gaps are plotted as zigzagline 510 in FIG. 6 providing a number of minimum sums and peak sums. Ifavailable, a user entered rotational speed is shown by line 512 in FIG.6. In order to determine which of the minimum sums is the actualrotational speed, peak sums at each of the rotational speed incrementsare summed in step 422 and plotted as line 514 on top of line 510. Therotational speed candidates having the higher peak sums are selected instep 424 as the most likely candidates for the actual rotational speed.In this case the highest peak sums are shown by the minimum associatewith point 516 in FIG. 6. While the foregoing is not an exactdetermination of the rotational speed, the most likely candidates takentogether with detailed information about the machine 120, such as numberof poles, number of gear teeth, and the like, is useful for determiningthe actual rotational speed of the machine 120.

In the third aspect, when the rotational speed is not represented withina measured harmonic spectrum, the first two aspects of the invention mayfail to identify a nominal rotational speed of the machine 120. Aprocedure 700 for using the analyzer according to this aspect of theinvention is illustrated in FIG. 7. Steps 702-710 are similar to steps152-160 of the first aspect of the invention and steps 402-410 of thesecond aspect of the invention and thus will not be repeated. In step712, an estimated rotational speed, and an accuracy value are selected.The estimated rotational speed can come from a customer, nameplateinformation on the machine, or a history of similar machines operatingunder similar conditions. The accuracy value (% Accuracy) is userselected value and may range from about 0.5 percent to about 2 percent.

Next, the spectrum is surveyed to locate the peaks in the spectrum instep 714 by the peak location method described above. In step 716, thelargest amplitude peaks of the located peaks in the spectrum areselected and the amplitude of the located largest peaks along with theirassociated frequencies are recorded. The number of largest peaks locatedin the spectrum is k wherein k ranges from 1 to K, and wherein K isinput by a user and must be less than or equal to the lines ofresolution of the spectrum divided by 4. The largest peaks provide thelocated amplitudes and associated frequencies to be considered forcalculating the rotational speed. The located frequencies are divided byinteger values from 1 through N in step 718 to provide divided values,wherein N is the maximum number of harmonics evaluated to find thelocated rotational speed. Candidate rotational speeds are designated bythe divided values that fall within the accuracy value of the estimatedrotational speed in step 720. Each of the candidate rotational speedsrepresents a harmonic family, and each candidate rotational speed andharmonic multiples thereof are scored based on their proximity to eachof the largest peaks.

A total score for each harmonic family is calculated in step 722 by tothe formula:Total Score=2−(Located frequency (k)/(n*candidate rotational speed(j))),wherein j the number of number of candidate rotational speeds and n isthe number of harmonic families considered.

The rotational speed is selected as the candidate rotational speed withthe highest score in step 724. If two or more candidate rotationalspeeds have the same highest score, then the candidate rotational speedfamily having the largest amplitude peak will produce the rotationalspeed.

Once the unknown rotational speed has been determined, the calculatedrotational speed can be used to help analyze the test frequencyspectrum, and thereby the characteristics of the machine. For example,the speed of a rotating shaft can be used with vibration informationsensed from the shaft to locate problems such as imbalance,misalignment, and bearing damage. Once these problems have beendiagnosed with the information, the technician can then correct theproblems. Thus, the method of determining rotational speed as describedis an important step in detecting, analyzing, and fixing problems withrotating equipment.

While preferred embodiments of the present invention are describedabove, it will be appreciated by those of ordinary skill in the art thatthe invention is capable of numerous modifications, rearrangements andsubstitutions without departing from the spirit of the invention.

The invention claimed is:
 1. A vibration analyzer for use in determininga nominal rotational speed of a rotating shaft, comprising: an input forsensing vibration signal data at an unknown rotational speed of theshaft, a memory for storing the vibrational signal data, a processorfor: producing a spectral plot of peaks in the vibrational data,receiving an estimated rotational speed, receiving an accuracy valuerelative to the estimated rotational speed, identifying a predeterminednumber (k) of largest peaks in the spectral plot, and recording alocated amplitude and associated frequency for each peak, creating a setof candidate rotational speeds by, dividing the located frequencies ofeach of the largest peaks by integer values of 1 through N, wherein N isa number of harmonics evaluated in order to calculate a rotationalspeed, to produce divided values for each of the located frequencies,and designating as candidate rotational speeds the divided values thatfall within the accuracy value relative to the estimated rotationalspeed, wherein each candidate rotational speed represents a harmonicfamily, scoring each candidate rotational speed based on a proximity ofthe candidate rotational speed and harmonic multiples of the candidaterotational speed to each of the largest peaks, and selecting as thenominal rotational speed the candidate rotational speed that has thehighest score.
 2. The vibration analyzer of claim 1, wherein theestimated rotational speed is a nameplate speed of the rotating shaft.3. The vibration analyzer of claim 1, wherein the accuracy value rangesfrom about 0.5 percent to about 2 percent.
 4. The vibration analyzer ofclaim 1, wherein the predetermined number (k) of largest peaks in thespectral plot ranges from 1 to K, wherein K is less than or equal toLOR/4, wherein LOR is lines of resolution of the spectral plot.
 5. Thevibration analyzer of claim 1, wherein N ranges from about 6 to no morethan Fmax/(estimated rotational speed), wherein Fmax is a maximumfrequency evaluated for a particular spectral plot.
 6. The vibrationanalyzer of claim 1, wherein the total score for each harmonic family iscalculated by to the formula:Total Score=2−(Located Frequency (k)/(n*candidate rotational speed(j))),wherein j is the number of number of candidate rotational speeds and nis the number of harmonic families considered.
 7. The vibration analyzerof claim 6, wherein the rotational speed is equivalent to the candidaterotational speed having the highest score.
 8. The vibration analyzer ofclaim 7, where if two or more candidate rotational speeds have the samescore, the rotational speed is determined as the candidate rotationalspeed with the largest score and having the largest located amplitudepeak as one of the members of the harmonic family.